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Lectures |
Table of Contents
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Astro 100 |
Black Holes and Neutron Stars
Outline
- Neutron Stars
- Black Holes
Terms to Know
neutron star
pulsar
black hole
Schwarzschild radius r=2GM/c2
event horizon
escape velocity
1. Neutron Stars
The incredibly dense material of white dwarfs is supported
by electron degeneracy (rather than gas pressure, as in main sequence stars).
What if you compress that material even further, e.g. by adding more mass
beyond the Chandrasekhar limit of 1.4 MSun? Will it really
collapse to a black hole?
It turns out there may be an intermediate step.
As you compress the material (made of densely-packed electrons and atomic
nuclei) further, you will eventually force the electrons to merge with protons
and form neutrons. The neutrons will be packed together almost touching,
with densities approaching the densities in atomic nuclei. A neutron
star is essentially one gigantic atomic nucleus, with very few protons
and very many neutrons. Neutron stars are supported by neutron degeneracy
pressure, similar to electron degeneracy pressure but at much much higher
density.
The major properties of neutron stars predicted
by theory include:
- masses up to about 3 MSun
- densities of around 2 x 1014 g/cm3; one
sugarcube would weigh the same as all of the 6 billion humans on Earth
- radii of around 10 km
- very fast rotation (think of a figure skater with arms pulled
in tight)
- very strong magnetic fields
The theoretical prediction of the existence of neutron
stars received a big boost with the discovery of pulsars in 1967. Pulsars
are objects that blink very fast in the radio (or optical) -- up to almost
1000 times per second. They are naturally explained by spinning neutron
stars with a beam of radiation that sweeps past the observer every rotation,
like a lighthouse beacon. Pulsars are often -- but not always -- observed
in supernova remnants.
So the whole theory hangs together: one probable
end for massive stars (M>7 MSun) after the red giant phase
is a supernova that leaves behind a neutron star core at the center of the
remnant. If the remaining core has a mass of more than about 3 MSun,
however, even neutron degeneracy pressure can't support the crushing weight
of material, and gravity finally wins...
2. Black Holes
- What is a black hole?
A black hole is any collection of matter that
is so dense that even light cannot escape its gravitational field. Note
that black holes don't have to be massive -- just dense!
How dense? Any mass M packed into a
radius smaller than r=2GM/c2 is a black hole. That radius
is called the Schwarzschild radius after the scientist who first calculated
it, and that location around the black hole is called the event horizon.
The idea is that as an object gets smaller and
smaller, you can get closer and closer to its center, so the force of gravity
(which goes as 1/r2) becomes stronger and stronger. As a result,
to escape the object's gravity, you would need to travel at a higher and
higher speed to avoid being pulled back to the surface. The speed at which
you can just barely escape from the surface is called the escape
velocity. (For example, at the Earth's surface, escape velocity is about
11 km/s -- which is how fast spaceships need to go to make it to the Moon
or beyond.) A black hole is an object with an escape velocity equal to or
greater than the speed of light.
Examples:
Object |
Mass |
Schwarzschild Radius |
Human |
7.5x104grams |
10-23 cm (less than a trillionth of a wavelength of green
light) |
Earth |
6x1027 grams |
0.9 cm |
Sun |
2x1023 grams |
3 km |
Massive Star |
2x1024 grams |
30 km |
Milky Way |
2x1034 grams |
.01 pc -- less than distance to Alpha Cen |
So if you could cram the entire Earth into a
golfball, it would be dense enough to constitute a black hole.
Note that the mass of Earth as it is now and
the mass of Earth compressed to the size of a golfball would be the same;
only the density would be different. At golfball size, the Earth would be
small enough that you could get very, very close to the center of gravity,
rather than being stuck far away, as we are now at the Earth's surface (r=6,000
km).
- What happens near a black hole?
Because black holes are small enough to let
you get close to them and fall under the influence of extraordinarily strong
gravitational forces, funny things start to happen.
Space itself gets distorted and curved very
near a black hole's event horizon. Since light travels through space --
like a ball rolling on a rubber sheet with a big weight on it -- light can
get bent by the strong gravitational field near a black hole. If the light
gets too close -- within the Schwarzschild radius -- it gets sucked in, never
to reappear. No information is available to the outside world on any events
happening within the event horizon.
If you were to fall head first into a 5 solar
mass black hole, you would be ripped apart by tidal forces (stronger pull
on head than on feet, so your head would be pulled off) long before you reached
the event horizon. Meanwhile, as your friends watched you, you'd seem to
fall slower and slower until finally you seemed to hang frozen in time.
You, on the other hand, would experience (if you could survive the tidal
forces, which you couldn't) a tremendous acceleration, but time would seem
to behave normally. As the matter of our bodies accelerated towards the
event horizon, it would heat up tremendously from the distortion, and would
start to shine brightly in X-rays.
- Where do black holes occur, and how do they form?
- What is the evidence for their existence?
- Fast motions in active galactic nuclei (AGN: quasars,
radio galaxies)
- Huge luminosity of AGN in tiny radius (brighter
than whole galaxy, but from volume the size of the solar system)
- Large masses of X-ray binary companion stars
in the Milky Way
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